Month: October 2014

HIPAD – A Hybrid Interior-Point Alternating Direction algorithm for knowledge-based SVM and feature selection

  • Ioannis G. Akrotirianakis
  • Zhiwei (Tony) Qin
  • Amit Chakraborty
  • Xiaocheng Tang
    • Categories Convex and Nonsmooth Optimization, Data-Mining, Quadratic Programming Tags , , , ,

    We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net support vector machine (SVM) through an alternating direction method of multipliers in the first phase, followed by an interior-point method … Read more

    Light on the Infinite Group Relaxation

  • Amitabh Basu
  • Robert Hildebrand
  • Matthias Köppe
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Cutting Plane Approaches

    This is a survey on the infinite group problem, an infinite-dimensional relaxation of integer linear optimization problems introduced by Ralph Gomory and Ellis Johnson in their groundbreaking papers titled “Some continuous functions related to corner polyhedra I, II” [Math. Programming 3 (1972), 23-85, 359-389]. The survey presents the infinite group problem in the modern context … Read more

    p-facility Huff location problem on networks

  • Rafael Blanquero
  • Emilio Carrizosa
  • Amaya Nogales-Gómez
  • Boglárka Tóth
    • Categories Applications - OR and Management Sciences, Network Optimization Tags , , , , ,

    The p-facility Huff location problem aims at locating facilities on a competitive environment so as to maximize the market share. While it has been deeply studied in the field of continuous location, in this paper we study the p-facility Huff location problem on networks formulated as a Mixed Integer Nonlinear Programming problem that can be … Read more

    Location and Allocation of Service Units on a Congested Network with Time Varying Demand Rates

  • Arjun Bhardwaj
  • Niraj Sinha
  • Navneet Vidyarthi
    • Categories Applications - OR and Management Sciences Tags , , , ,

    The service system design problem arises in the design of telecommunication networks, refuse collection and disposal networks in public sector, transportation planning, and location of emergency medical facilities. The problem seeks to locate service facilities, determine their capacities and assign users to those facilities under time varying demand conditions. The objective is to minimize total … Read more

    Semi-definite relaxations for optimal control problems with oscillation and concentration effects

  • Mathieu Claeys
  • Didier Henrion
  • Martin Kružík
    • Categories Control Applications, Semi-definite Programming

    Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phenomena, by relaxing controls as Young measures. These semi-definite relaxations were later on extended to optimal control problems depending linearly on the control input and typically featuring concentration phenomena, interpreting the control as a measure of time with a … Read more

    Hedging Problem

  • Xuyan Wang
    • Categories Finance and Economics, Global Optimization Applications

    For index-based hedging design, the scatter plot of the hedging contract losses versus the losses to be hedged is generally used to visualize and quantify basis risk. While studying this scatter plot, which does not cluster along the diagonal as desired, a “bundled loss” phenomenon is found. In a setting where both the hedging and … Read more

    Globally Convergent Primal-Dual Active-Set Methods with Inexact Subproblem Solves

  • Frank E. Curtis
  • Zheng Han
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Quadratic Programming Tags , , , , ,

    We propose primal-dual active-set (PDAS) methods for solving large-scale instances of an important class of convex quadratic optimization problems (QPs). The iterates of the algorithms are partitions of the index set of variables, where corresponding to each partition there exist unique primal-dual variables that can be obtained by solving a (reduced) linear system. Algorithms of … Read more

    A Polynomial-Time Affine-Scaling Method for Semidefinite and Hyperbolic Programming

  • James Renegar
  • Mutiara Sondjaja
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    We develop a natural variant of Dikin’s affine-scaling method, first for semidefinite programming and then for hyperbolic programming in general. We match the best complexity bounds known for interior-point methods. All previous polynomial-time affine-scaling algorithms have been for conic optimization problems in which the underlying cone is symmetric. Hyperbolicity cones, however, need not be symmetric. … Read more

    Rectangular sets of probability measures

  • Alexander Shapiro
    • Categories Stochastic Programming Tags , , , , , ,

    In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider (2003), from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent … Read more

    Nonlinear local error bounds via a change of metric

  • Dominique Azé
  • Jean-Noël Corvellec
    • Categories Convex and Nonsmooth Optimization, Infinite Dimensional Optimization, Nonlinear Optimization Tags , ,

    In this work, we improve the approach of Corvellec-Motreanu to nonlinear error bounds for lowersemicontinuous functions on complete metric spaces, an approach consisting in reducing the nonlinear case to the linear one through a change of metric. This improvement is basically a technical one, and allows dealing with local error bounds in an appropriate way. … Read more